The Electoral college system
Each state is assigned a certain number of electoral votes based on their population. For example, Kansas has 6 electors in the electoral college. So, in the last election, Donald Trump won the popular vote of Kansas, thus all 6 electors from Kansas went to Donald Trump. The same policy goes for every other state except Maine and Nebraska, who, instead of giving all electors to one candidate, may split based on the ratio.
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If you are referring to the President and Vice President, they are elected by the Electoral College according to majority popular vote in each state (this policy is not applicable in Nebraska where the electoral votes are split by percentage inside the state). If you are referring to the Secretaries of the Cabinet Departments, they are appointed by the President upon assuming office. If the President wishes to reappoint the same Cabinet member as his predecessor, there is no further process. If he wishes to appoint somebody new, he must present the candidate to the Senate for a confirmation requiring 2/3 of the Senate to approve the appointment.
Popular Sovereignty
Yes, the Gandhi's policy of non-cooperation popular in India.
Joe Bidden
Antebellum South Carolina had a policy of sending electors to the Electoral College based on the voting in the state legislature.
Party identification, policy preferences, and candidate's valence.
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